Enhanced hydrogen-gas permeation through rippled graphene

Wenqi Xiong, Weiqing Zhou, Pengzhan Sun, and Shengjun Yuan

Phys. Rev. B 108, 045408 – Published 17 July 2023

Abstract

The penetration of atomic hydrogen through defect-free graphene was generally predicted to have a barrier of at least several eV, which is much higher than the 1-eV barrier measured for hydrogen-gas permeation through pristine graphene membranes. Herein, our density functional theory calculations show that ripples, which are ubiquitous in atomically thin crystals and mostly overlooked in the previous simulations, can significantly reduce the barriers for all steps constituting the mechanism of hydrogen-gas permeation through graphene membranes, including dissociation of hydrogen molecules, reconstruction of the dissociated hydrogen atoms and their flipping across graphene. Especially, the flipping barrier of hydrogen atoms from a cluster configuration is found to decrease rapidly down to $< 1 eV$ with increasing ripples' curvature. The estimated hydrogen permeation rates by fully considering the distribution of ripples with all realistic curvatures and the major reaction steps that occurred on them are quite close to the experimental measurements. Our work provides insights into the fundamental understanding of hydrogen-gas permeation through graphene membranes and emphasizes the importance of nanoscale nonflatness (ripples) in explaining many surface and transport phenomena (for example, functionalization, corrosion and separation) in graphene and other two-dimensional materials.

Received 6 April 2023
Revised 5 May 2023
Accepted 26 June 2023

DOI:https://doi.org/10.1103/PhysRevB.108.045408

Physics Subject Headings (PhySH)

First-principles calculations

Graphene

Ab initio molecular dynamics Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wenqi Xiong^1,*, Weiqing Zhou^1,*, Pengzhan Sun^2,†, and Shengjun Yuan ^1,3,‡

¹Key Laboratory of Artificial Micro- and Nano-structures of the Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
²Joint Key Laboratory of the Ministry of Education, Institute of Applied Physics and Materials Engineering, University of Macau, Avenida da Universidade, Taipa, Macau 999078, China
³Wuhan Institute of Quantum Technology, Wuhan 430206, China

^*These authors contributed equally to this work
^†pengzhansun@um.edu.mo
^‡s.yuan@whu.edu.cn

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Issue

Vol. 108, Iss. 4 — 15 July 2023

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Images

Figure 1
(a) A schematic illustrating the major elementary steps constituting the mechanism of hydrogen permeation through graphene membranes, if local curvature is considered. (b) Time evolution of position changes for the selected carbon atoms (C1 and C2, color coded) due to thermal fluctuations. C1 and C2 are carbon atoms at the central positions and occupied by hydrogen, as illustrated in the inset. (c) Typical snapshots for the convex and concave regions of a freestanding graphene membrane captured at 300 K. The membrane is deliberately adsorbed with hydrogen adatoms. The black arrows point to atoms C1 and C2 in (b) whose vertical positions change over time. (d) Distribution of charge density for flat (left) and rippled (right) graphene. Isosurface, $0.3 e / B o h r^{3}$ . The arrow refers to the direction of electron transfer, from concave to convex.
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Figure 2
(a) Dissociation of $H_{2}$ at the central positions of flat and rippled $(t / D = 12 %)$ graphene (color coded). Insets: atomic configurations of initial (IS), transition (TS), and final (FS) states, respectively. Dissociation barrier $E_{b}$ and chemisorption energy $E_{c}$ are illustrated on the energy profile. (b) $E_{b}$ (left $y$ axis) and $E_{c}$ (right) as a function of the ripple's curvature $t / D$ (illustrated in the inset) for dissociation of $H_{2}$ at the central position of graphene. Inset: the ripple's curvature is characterized by the ratio $t / D$ of its height $t$ to diameter $D$ . Positive (negative) values represent a convex (concave) shape. Dashed lines are guides to the eyes. The potential energy surface (PES) for dissociation of $H_{2}$ on (c) flat and (d) rippled $(t / D = 12 %)$ graphene as a function of the distance between two H atoms in the dissociated molecule $(d_{H - H})$ and their distance to the central adsorption sites of the lattice $(d_{H - C})$ . The dashed lines are the minimum energy paths along the reaction path. (e) The energy gain of $H_{2}, E_{b}^{H - H}$ , with increasing $d_{H - H}$ from its equilibrium value of 0.75 Å. The bond length measured at TS for $t / D = 0$ and 12% are labeled. (f) At different curvatures $t / D, d_{H - H}$ measured at TS, and the resulting $E_{b}^{H - H}$ obtained from (c) are compared with the total energy barrier $E_{b}$ obtained from (b). Dashed lines are guides to the eyes.
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Figure 3
(a) Desorption and diffusion barriers of hydrogen adatoms on convex, flat and concave surfaces. Insets: schematics for the desorption and diffusion processes on concave and convex surfaces. (b) Energy profiles for the desorption (left) and diffusion (right) of H atoms over a concave ripple $(t / D = - 12 %)$ . Insets illustrate the desorption and diffusion processes with the arrows showing the moving direction of H atoms. (c) Left panel: schematic diagram of the sequential readsorption of four hydrogen atoms. Blue dashed arrows indicate the moving direction of H atoms. Right panel: energy evolution of the readsorption reaction for convex $(t / D = + 12 %)$ , flat and concave $(t / D = - 12 %)$ surfaces (from top to bottom). The term ‘ $n H$ ’ $(n = 1$ to 4) denotes the number of H atoms being adsorbed on the hexatomic ring.
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Figure 4
(a) Examples of the local cluster configurations with number of hydrogen atoms $n = 194$ and corresponding flipping barriers. (b) The flipping barriers for the four-hydrogen configuration at different curvatures. Symbols: calculated data. Solid line: best linear fit. Inset: energy profile at $t / D = 12 %$ .
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Figure 5
(a) Ripple density as a function of curvature $t / D$ at different $T$ (color coded). The data are cited from Ref. [44]. Upper inset: same data as in the main panel but in a linear $y$ scale. Lower inset: a typical snapshot of a graphene membrane at 300 K from molecular dynamics simulations. (b) Calculated hydrogen permeation rates at different $T$ by considering the ripple distribution in (a) and assuming flipping as the main rate-limited step. Green symbols: calculated data at different $T$ . Red symbols: experimental data cited from Ref. [11]. Upper inset: zoom-in for the experimentally relevant $T$ range. Lower inset: schematics for the hydrogen permeation process including dissociation and flipping.
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